About one problem of finding equal strength contour inside a viscoelastic rectangle

• Autorzy: Kapanadze Giorgi , Kipiani Gela , Rajczyk Marlena

Identyfikatory

DOI

10.17512/znb.2023.1.06

Warianty tytułu

PL

O problemie znalezienia konturu stałej wytrzymałości wewnątrz lepkosprężystego prostokąta

• Języki publikacji: EN

Abstrakty

EN

The problem of finding an equal-strength contour inside a viscoelastic rectangle according to the Kelvin-Voigt model is considered. It is assumed that constant normal compressive forces with given principal vectors act on the sides of the rectangle (or the values of constant normal displacements are known), and the inner boundary (the desired equal-strength contour) is free from external forces. The methods of the theory of conformal reflections, Cauchy type integral and boundary value problems of analytic functions are used to study the plate bending problems discussed in the paper. Which in turn are based on the task of constructing a conformally mapping function on a doubly linked circular ring bounded by broken line. The latter is reduced to the Riemann-Hilbert problem for a circular ring based on the solution of which it becomes possible to present the mentioned function in a defective form. It is worth noting that when considering mixed problems of plate bending for doubly connected areas bounded by broken line, it is possible to decompose them into two independent problems, each of which is a Riemann-Hilbert problem.

PL

Rozważono problem znalezienia konturu o stałej wytrzymałości wewnątrz lepko sprężystego prostokąta zgodnie z modelem Kelvina-Voigta. Zakłada się, że na boki prostokąta działają stałe normalne siły ściskające o danych wektorach głównych (lub znane są wartości stałych przemieszczeń normalnych), a wewnętrzna granica (żądany kontur o jednakowej wytrzymałości) jest wolna od sił zewnętrznych. Do badania omawianych w artykule problemów zginania płyt wykorzystano metody teorii odbić konforemnych, zagadnienia całki typu Cauchy’ego i wartości brzegowych funkcji analitycznych, które z kolei opierają się na zadaniu skonstruowania funkcji odwzorowującej konformalnie na podwójnie połączonym pierścieniu kołowym ograniczonym linią przerywaną. To ostatnie sprowadza się do problemu Riemanna-Hilberta dla pierścienia kołowego na podstawie rozwiązania, które możliwe jest jako przedstawienie wspomnianej funkcji w postaci wadliwej. Warto zauważyć, że rozpatrując mieszane problemy zginania blachy dla obszarów podwójnie połączonych ograniczonych linią przerywaną, można je rozłożyć na dwa niezależne problemy, z których każdy jest problemem Riemanna-Hilberta.

Słowa kluczowe

EN

Kelvin-Voigt model; Volterra equation; Kolosov Muskhelishvili formulas; Riemann-Hilbert problem

PL

model Kelvina-Voigta; wzór Kolosova-Mushelishvili; problem Riemanna-Hilberta; równanie Volterra

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo
• Rocznik: 2023
• Tom: Z. 29 (179)
• Strony: 41--47
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Kapanadze Giorgi

• Ivane Javakhishvili Tbilisi State University, Ilia Chavchavadze Avenue, Tbilisi 0179, Georgia

autor

Kipiani Gela

• The Department of Engineering Mechanics and Construction, Georgian Technical University, Kostava Str., Tbilisi 0171, Georgia

• https://orcid.org/0000-0001-6811-3595

autor

Rajczyk Marlena

• Czestochowa University of Technology, Faculty of Civil Engineering, ul. Akademicka 3, 42-218 Częstochowa, Poland

• https://orcid.org/0000-0002-4893-0931

Bibliografia

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• 17. Kapanadze G., Kakhaia K., Kipiani G., On one inverse task of variable stiffness plate bending, Georgian Engineering News 2006, 3, 35-38.
• 18. Churchelauri Z., Kipiani G., Calculation of thin-walled prefabricated type shells with model of plastic-rigid body, Selected, blind peer reviewed papers from 7th International Conference on Contemporary Problems of Architecture and Construction. November 19th-21st, 2015, Florence 2015, 19-24.
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).